L4

Recent progress in the development of equivariant neural network architectures predominantly used for machine learning interatomic potentials (MLIPs) has opened new possibilities in the development of data-driven coarse-graining strategies. In this talk, I will first present our work on the development of learning potential energy surfaces and other physical quantities, namely the Hyperactive Learning framework[1], a Bayesian active learning strategy for automatic efficient assembly of training data in MLIP and ACEfriction [2], a framework for equivariant model construction based on the Atomic Cluster Expansion (ACE) for learning of configuration-dependent friction tensors in the dynamic equations of molecule surface interactions and Dissipative Particle Dynamics (DPD). In the second part of my talk, I will provide an overview of our work on the simulation and analysis of Generalized Langevin Equations [3,4] as obtained from systematic coarse-graining of Hamiltonian Systems via a Mori-Zwanzig projection and present an outlook on our ongoing work on developing data-driven approaches for the construction of dynamics-preserving coarse-grained representations.

References:

[1] van der Oord, C., Sachs, M., Kovács, D.P., Ortner, C. and Csányi, G., 2023. Hyperactive learning for data-driven interatomic potentials. npj Computational Materials

[2] Sachs, M., Stark, W.G., Maurer, R.J. and Ortner, C., 2024. Equivariant Representation of Configuration-Dependent Friction Tensors in Langevin Heatbaths. to appear in Machine Learning: Science & Technology

[3] Leimkuhler, B. and Sachs, M., 2022. Efficient numerical algorithms for the generalized Langevin equation. SIAM Journal on Scientific Computing

[4] Leimkuhler, B. and Sachs, M., 2019. Ergodic properties of quasi-Markovian generalized Langevin equations with configuration-dependent noise and non-conservative force. In Stochastic Dynamics Out of Equilibrium: Institut Henri Poincaré, 2017 

The epithelial to mesenchymal transition (EMT) is a key cellular process underlying cancer progression, with multiple intermediate states whose molecular hallmarks remain poorly characterized. In this talk, I will describe AI-powered and ecology-inspired methods recently developed by us to provide a multi-scale view of the epithelial-mesenchymal plasticity in cancer from single cell and spatial transcriptomics data. First, we employed a large language model similar to the one underlying chatGPT but tailored for biological data (inspired by scBERT methodology), to predict individual stable states within the EMT continuum in single cell data and dissect the regulatory processes governing these states. Secondly, we leveraged spatial transcriptomics of breast cancer tissue to delineate the spatial relationships between cancer cells occupying distinct states within the EMT continuum and various hallmarks of the tumour microenvironment. We introduce a new tool, SpottedPy, that identifies tumour hotspots within spatial transcriptomics slides displaying enrichment in processes of interest, including EMT, and explores the distance between these hotspots and immune/stromal-rich regions within the broader environment at flexible scales. We use this method to delineate an immune evasive quasi-mesenchymal niche that could be targeted for therapeutic benefit. Our insights may inform strategies to counter immune evasion enabled by EMT and offer an expanded view of the coupling between EMT and microenvironmental plasticity in breast cancer.

Tumour microenvironment is characterised by heterogeneity at various scales: from various cell populations (immune cells, cancerous cells, ...) and various molecules that populate the microenvironment (cytokines, chemokines, extracellular vesicles, …); to phenotype heterogeneity inside the same cell population (e.g., immune cells with different phenotypes and different functions); as well as temporal heterogeneity in cells’ phenotypes (as cancer evolves through time) and spatial heterogeneity.
In this talk we overview some mathematical models and computational approaches developed to investigate different single-scale and multi-scale aspects related to heterogeneous immune responses during cancer evolution. Throughout the talk we emphasise the qualitative vs. quantitative results, and data availability across different scales

Understanding how living systems dynamically self-organise across spatial and temporal scales is a fundamental problem in biology; from the study of embryo development to regulation of cellular physiology. In this talk, I will discuss how we can use mathematical modelling to uncover the role of microscale physical interactions in cellular self-organisation. I will illustrate this by presenting two seemingly unrelated problems: environmental-driven compartmentalisation of the intracellular space; and self-organisation during collective migration of multicellular communities. Our results reveal hidden connections between these two processes hinting at the general role that chemical regulation of physical interactions plays in controlling self-organisation across scales in living matter

In this talk I will give a number of short vignettes of work that has been undertaken in my group over the last 15 years. Mathematically, the theme that underlies our work is the importance of randomness to biological systems. I will explore a number of systems for which randomness plays a critical role. Models of these systems which ignore this important feature do a poor job of replicating the known biology, which in turn limits their predictive power. The underlying biological theme of the majority our work is development, but the tools and techniques we have built can be applied to multiple biological systems and indeed further afield. Topics will be drawn from, locust migration, zebrafish pigment pattern formation, mammalian cell migratory defects, appropriate cell cycle modelling and more. I won't delve to deeply into anyone area, but am happy to take question or to expand upon of the areas I touch on.

Deep learning algorithms provide unprecedented opportunities to characterise complex structure in large data, but typically in a manner that cannot easily be interpreted beyond the 'black box'. We are developing methods to leverage the benefits of deep generative learning and computational modelling (e.g. fluid dynamics, solid mechanics, biochemistry), particularly in conjunction with biomedical imaging, to enable new insights into disease to be made. In this talk, I will describe our applications in several areas, including modelling drug delivery in cancer and retinal blood vessel loss in diabetes, and how this is leading us into the development of personalised digital twins.

I will present TeXmacs (www.texmacs.org), a document preparation system with structured editing and high quality typography, designed to create technical documents. 

For more details see https://mgubi.github.io/docs/programming.html

We investigate a stochastic differential game in which a major player has a private information (the knowledge of a random variable), which she discloses through her control to a population of small players playing in a Nash Mean Field Game equilibrium. The major player’s cost depends on the distribution of the population, while the cost of the population depends on the random variable known by the major player. We show that the game has a relaxed solution and that the optimal control of the major player is approximatively optimal in games with a large but finite number of small players. Joint work with Pierre Cardaliaguet and Catherine Rainer.